Interesting question. You might want to be more explicit about exactly what characteristics you want in this distribution, i.e. what phenomenon generates your data. For example, I'm not a physicist, but for beams of particles with varying intensities hitting a detector plate subject to random noise:

• Cluster means distributed uniformly over a rectangular area.
• Number of points per cluster following an exponential distribution (or whatever the beam intensities follow).
• Points in each cluster distributed as a 2D Gaussian. (With variance fixed or chosen according to some distribution?)
• Number of clusters either fixed or chosen according to some distribution.

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